From Conditionality to Modality in Luganda (Bantu, JE15): a Synchronic and Diachronic Corpus Analysis of the Verbal Prefix-Andi

Total Page:16

File Type:pdf, Size:1020Kb

From Conditionality to Modality in Luganda (Bantu, JE15): a Synchronic and Diachronic Corpus Analysis of the Verbal Prefix-Andi Journal of Pragmatics 127 (2018) 84e106 Contents lists available at ScienceDirect Journal of Pragmatics journal homepage: www.elsevier.com/locate/pragma From conditionality to modality in Luganda (Bantu, JE15): A synchronic and diachronic corpus analysis of the verbal prefix-andi- * Deo Kawalya a, Gilles-Maurice de Schryver b, c, , Koen Bostoen b a School of Languages, Literature and Communication, Makerere University, PO Box 7062, Kampala, Uganda b BantUGent e UGent Centre for Bantu Studies, Department of Languages and Cultures, Ghent University, Rozier 44, 9000 Ghent, Belgium c Department of African Languages, University of Pretoria, 0002 Pretoria, South Africa article info abstract Article history: This article offers a synchronic and diachronic analysis of the use and meaning of the Received 29 November 2016 verbal prefix-andi- in the Great Lakes Bantu language Luganda (JE15). On the basis of a text Received in revised form 18 January 2018 corpus of 4 million tokens, we show that the prefix, commonly described as a conditional Accepted 29 January 2018 marker, is primarily involved in the expression of modal meanings, specifically deontic Available online 23 February 2018 necessity and epistemic possibility. Our thirteen-decade diachronic corpus analysis shows that there is a relationship between the increased use of -andi- outside syntactically Keywords: complex conditional constructions, i.e. those having both a protasis and an apodosis, and Modality Conditionality an increase in its expression of modal meanings. Moreover, a reduction in the use of -andi- Protasis in complex conditional constructions goes hand in hand with a reduction in its expression Apodosis of conditional meanings. It is further revealed that contrary to the common cross-linguistic Diachronic corpus study tendency to rely on modality as a source for conditionality, the conditional meaning of Luganda -andi- is not post-modal. Instead it was primarily a conditional marker, which subse- quently developed different modal meanings. © 2018 Elsevier B.V. All rights reserved. 1. Introduction 1.1. On the interplay between conditionality and modality Several typological studies have dealt with conditionality as a meaning typically originating in modality (Bybee et al.,1994; Traugott, 1985), more specifically as a post-modal destination for either epistemic possibility or epistemic necessity (van der Auwera and Plungian, 1998: 98). In Bantu linguistics, the historical relationships between modal and conditional markers have not raised much interest so far. Modality and conditionality have at best each been dealt with in isolation. In this article, we show that the Ugandan Bantu language Luganda has a verbal prefix-andi- that is neither a dedicated conditional marker nor a dedicated modal marker, contrary to what has been described in the literature. As we show on the basis of a Luganda text corpus, it currently straddles the semantic domains of modality and conditionality. What is more, we argue, by means of a * Corresponding author. BantUGent e UGent Centre for Bantu Studies, Department of Languages and Cultures, Ghent University, Rozier 44, 9000 Ghent, Belgium. E-mail addresses: [email protected], [email protected] (D. Kawalya), [email protected] (G.-M. de Schryver), koen.bos- [email protected] (K. Bostoen). https://doi.org/10.1016/j.pragma.2018.01.011 0378-2166/© 2018 Elsevier B.V. All rights reserved. D. Kawalya et al. / Journal of Pragmatics 127 (2018) 84e106 85 Abbreviations and symbols APPL applicative AUGx augment of class x CF counterfactual(ity) CONN connective DEMa proximal demonstrative DEMb medial demonstrative DeNe deontic necessity EPo epistemic possibility FV final vowel H high tone HYP hypothetical(ity) INFj infinitive IPFV imperfective LOCx locative of class x N homorganic nasal NEAR_FUT near future NEAR_PST near past NEG negative NEUT neuter NPx nominal prefix of class x Ø zero/empty morph OPx object prefix of class x PASS passive PFVj perfective PL plural POSSx possessive of class x PPx pronominal prefix of class x PRS present RECP reciprocal REFL reflexive RELx relative of class x REM_FUT remote future REM_PST remote past SG singular SPx subject prefix of class x TA(M) Tense, Aspect (, Modality) UNR the unreality marker -andi- diachronic corpus analysis, that the conditional meaning of -andi- is not post-modal. Quite the contrary, it used to be pri- marily a conditional marker, which subsequently developed different modal meanings, such as deontic necessity and epistemic possibility. In other words, we present here language-specific counterevidence for the common cross-linguistic tendency to rely on modality as a source for conditionality. 1.2. On conditionality Various definitions and typologies of conditionals exist (see Comrie, 1986; Dancygier, 1993,1998; Declerck and Reed, 2001; Salone, 1979; Sweetser, 1990, among others). This is partly due to the large number of criteria that can be used to categorize and interpret conditionals. Formulating a precise and universally applicable definition of conditionals has proven to be extremely difficult, not to say impossible (Declerck and Reed, 2001: 8). Proposing such a definition is neither an aim nor a necessary condition for the current study. We have deemed it more meaningful to first present those typologies of condi- tionality that have informed our research on Luganda conditionals as it proceeded. A classic and widely used distinction is the one between simple, hypothetical and counterfactual conditionals. It also underlies the work of Salone (1979) on Haya (JE22), a Tanzanian Bantu language closely related to Luganda, which is one of the rare dedicated studies on conditionals in Bantu, along with his subsequent dissertation on conditionals in Swahili (G42d) (Salone,1983a ). For simple conditionals, he states that “a proposition results if another proposition holds”, as shown in (1) and (2). Hypothetical conditionals, as in (3), on the other hand, are those “in which the antecedent introduces a hypothetical or 86 D. Kawalya et al. / Journal of Pragmatics 127 (2018) 84e106 imaginary proposition (where that proposition is not assumed to be false)”. Counterfactual conditionals refer to “sentences in which the antecedent asserts a proposition which is assumed to be false”, as in (4). Salone (1979) further adopts another common distinction, i.e. between ‘real’ and ‘unreal’ conditionals. Semantically, so-called ‘Unreality Conditionals’ include future simple conditionals (2), hypotheticals (3) and counterfactuals (4). Structurally, however, future simple conditionals (2) do not make use of a syntactic marker of unreality, unlike other semantic types of unreal conditionals. Hence, syntactically, they resemble semantically real conditionals, such as the simple present conditional in (1). (1) If the sun shines, the birds sing. (2) If you go to the store, I will cook. (3) If I saw Sidney Poitier in person, I'd faint. (4) If he had cooked, I would have eaten. (Salone, 1979: 65;66) Another often cited definition is the one by Comrie (1986: 78) who conceives conditionals from a logical perspective as “a relation between two propositions, the protasis (p) and the apodosis (q), such that either p and q are both true, or p is false and q is true, or p is false and q is false; excluded is the possibility of p being true and q is false.” In his attempt at a cross- linguistic characterization of conditionals, he adds, as a further restriction to his definition in natural language, that “the content of the protasis must be interpretable as a cause of the content of the apodosis” (Comrie, 1986: 80). He identifies four major parameters necessary for the description and categorization of conditionals; namely clause order, marking of condi- tionality, degrees of hypotheticality and time reference. In contrast to Comrie's basically semantic definition, Dancygier (1993: 403), whose work we have only discovered in the course of writing the current article, primarily defines a conditional in formal-structural terms as “a complex sentence composed of the main clause (q, or the apodosis) and a subordinate clause (p, or the protasis) introduced by a conditional conjunction, which in the majority of conditional sentences in English is if” (see also Dancygier, 1998: 1). Two parameters inform this English-based definition, viz. the presence of if, which signals the speaker's non-assertiveness of the assumption in the protasis and the syntactic frame if p, then q, which signals a semantic or pragmatic relation between p and q, whereby q can only be asserted after assuming p. Dancygier further subdivides conditionals on functional grounds into predictive and non-predictive conditionals. Formally, predictive conditionals are characterized in terms of backshift, that is, “the time reference intended by the speaker is systematically later than the time referred to by the verb form in its prototypical (non- conditional) uses” (Dancygier, 1993: 406). Semantically, clauses in predictive conditional constructions are said to exhibit sequential and causal relations, such that the proposition in the protasis precedes the proposition in the apodosis (Dancygier, 1993: 412). All sentences in (1) to (4) above are classified as predictive in Dancygier's typology; in addition to all of them exhibiting sequential and causal relations, (2) to (4) also exhibit backshift. Sentence (5) is an example of a non-predictive conditional. In such conditionals, the kind of backshift exhibited in pre- dictive conditionals does not occur. In this sentence, the verb forms refer to the time that they indicate; the verb in the protasis is in the present and it also refers to the present, while the verb in the apodosis indicates past and also refers to the past. (5) If she is in the lobby, the plane arrived early. (Dancygier, 1993: 415) In non-predictive conditionals, there is also a lack of content relation between the assumptions expressed in the clauses. In conditional constructions like (5), where events are presented in reversed chronological order, causality cannot arise according to Dancygier (1993: 423), because no sequentiality of events is indicated by the sequence of clauses.
Recommended publications
  • The Information Status of English If-Clauses in Natural Discourse*
    The Information Status of English If-clauses in Natural Discourse* Chang-Bong Lee 1. Introduction Haiman (1978) once argued that conditionals are uniformly defined as topics. His argument had to suffer from some substantial problems both empirically and theoretically. Despite these problems, his paper was a trailblazing research that opened up the path for the study of conditionals from a discourse point of view. The present paper studies conditionals from a particular aspect of discourse functional perspective by analyzing the information structure of conditional sentences in natural discourse. Ford and Thompson (1986) studied the discourse function of conditionals in the similar vein through a corpus-based research. This paper also attempts to understand the discourse function of conditionals, but it does it under a rather different standpoint, under the framework of the so-called GIVEN-NEW taxonomy as presented in Prince (1992). In this paper, we focus on the definition of topic as an entity that represents the GIVEN or OLD information to be checked against the information in the preceding linguistic context. By analyzing the data of the English if-clauses in natural discourse both in oral and written contexts, we present sufficient evidence to show that conditionals are not simply topics (GIVEN information). It is revealed that the if-clauses *This research was supported by the faculty settlement research fund (Grant No. 20000005) from the Catholic University of Korea in the year of 2000. I wish to express gratitude to the Catholic University of Korea for their financial assistance. The earlier version of this paper was presented at the 6th academic conference organized by the Discourse and Cognitive Ilnguistics Society of Korea in June, 2000.
    [Show full text]
  • Understanding Conditional Sentences
    GRAMMAR AND MECHANICS Understanding Conditional Sentences When a dependent or subordinate clause is introduced by words such as “if,” “when,” or “unless,” the complete sentence expresses a condition. The dependent or subordinate clause states a condition or cause and is joined with an independent clause, which states the result or effect. Conditional sentences can be factual, predictive, or speculative, which determines the form of the condition and the choice of verb tenses. TYPES OF CONDITIONAL SENTENCES Factual In a factual conditional sentence, the relationship between the dependent or subordinate clause and the independent clause describes a condition that is or was habitually true: if the condition applies, the independent clause states the result or effect. Both clauses use simple verb forms either in present or past tense. If you find a blue and white sweater, it belongs to me. When he plays his music too loud, the neighbors complain. Unless there is a question, the class is dismissed. Predictive In a predictive conditional sentence, the relationship between the two clauses is promised or possible but not certain. Use a present-tense verb in the dependent or subordinate clause, and in the independent clause use modal auxiliaries “will,” “can,” “may,” “should,” or “might” with the base form of the verb. If the weather is good tomorrow, we will go to the park. If your roommate decides not to come with us, we can go by ourselves. When the lease on the apartment ends, we may want to move to another building. When she misses one of the meetings, she should notify her supervisor.
    [Show full text]
  • Conditionals in Political Texts
    JOSIP JURAJ STROSSMAYER UNIVERSITY FACULTY OF HUMANITIES AND SOCIAL SCIENCES Adnan Bujak Conditionals in political texts A corpus-based study Doctoral dissertation Advisor: Dr. Mario Brdar Osijek, 2014 CONTENTS Abstract ...........................................................................................................................3 List of tables ....................................................................................................................4 List of figures ..................................................................................................................5 List of charts....................................................................................................................6 Abbreviations, Symbols and Font Styles ..........................................................................7 1. Introduction .................................................................................................................9 1.1. The subject matter .........................................................................................9 1.2. Dissertation structure .....................................................................................10 1.3. Rationale .......................................................................................................11 1.4. Research questions ........................................................................................12 2. Theoretical framework .................................................................................................13
    [Show full text]
  • Towards a Pragmatic Category of Conditionals
    19th ICL papers Chi-He ELDER and Kasia M. JASZCZOLT University of Cambridge, United Kingdom [email protected], [email protected] Conditional Utterances and Conditional Thoughts: Towards a Pragmatic Category of Conditionals oral presentation in session: 6B Pragmatics, Discourse and Cognition (Horn & Kecskes) Published and distributed by: Département de Linguistique de l’Université de Genève, Rue de Candolle 2, CH-1205 Genève, Switzerland Editor: Département de Linguistique de l’Université de Genève, Switzerland ISBN:978-2-8399-1580-9 Travaux du 19ème CIL | Travaux 20-27 Juillet 2013 Genève des Linguistes, International Congrès 20-27 July 2013 Geneva of Linguists, Congress International 1" " Conditional Utterances and Conditional Thoughts: Towards a Pragmatic Category of Conditionals Chi-Hé Elder and Kasia M. Jaszczolt Department of Theoretical and Applied Linguistics University of Cambridge Cambridge CB3 9DA United Kingdom [email protected] [email protected] 1. Rationale and objectives The topic of this paper is the pragmatic and conceptual category of conditionality. Our primary interest is how speakers express conditional meanings in discourse and how this diversity of forms can be accounted for in a theory of discourse meaning. In other words, we are concerned not only with conditional sentences speakers utter in discourse (sentences of the form ‘if p (then) q’), but predominantly with conditional thoughts, expressed in a variety of ways, by discourse participants. The category of conditionality has given rise to many discussions and controversies in formal semantics, cognitive semantics and post-Gricean pragmatics. In formal semantics, pragmatic considerations have often been appealed to in order to demonstrate that conditionals in natural language do, or do not, essentially stem out of material conditionals on the level of their logical form.
    [Show full text]
  • Dissertations, Department of Linguistics
    UC Berkeley Dissertations, Department of Linguistics Title A Cognitive Approach to Mandarin Conditionals Permalink https://escholarship.org/uc/item/5qw934z5 Author Yang, Fan-Pei Publication Date 2007 eScholarship.org Powered by the California Digital Library University of California A Cognitive Approach To Mandarin Conditionals By Fan-Pei Gloria Yang B.A. (National Taiwan Normal Univeristy) 1998 M.A. (University of California, Berkeley) 2003 A dissertation submitted in partial satisfaction of the Requirements for the degree of Doctor of Philosophy in Linguistics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Eve Sweetser, Chair Professor George Lakoff Professor Jerome Feldman Spring 2007 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A Cognitive Approach To Mandarin Conditionals Copyright © 2007 By Fan-Pei Gloria Yang Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract A Cognitive Approach To Mandarin Conditionals By Fan-Pei Gloria Yang Doctor of Philosophy in Linguistics University of California, Berkeley Professor Eve Sweetser, Chair This dissertation provides a description of some of the common Mandarin conditional constructions, with a focus on describing the contributions of the linking devices to the conditional interpretations and their interactions with other elements in constructions. The analyses are based on corpus data and include studies on the pragmatic uses of conditionals. The discussion endeavors to show how cognitive structures link to linguistic structures and how spaces are built and frames evoked. Consequently, the research does not just provide a syntactic description, but offers an in-depth discussion of epistemic stance and grounding of information indicated by the linking devices.
    [Show full text]
  • Robert C. Stalnaker*
    ROBERT C. STALNAKER* A THEORY OF CONDITIONALS I. INTRODUCTION A conditional sentence expresses a proposition which is a function of two other propositions, yet not one which is a truth function of those prop­ ositions. I may know the truth values of "Willie Mays played in the American League" and "Willie Mays hit four hundred" without knowing whether or not Mays. would have hit four hundred if he had played in the American League. This fact has tended to puzzle, displease, or delight philosophers, and many have felt that it is a fact that calls for some comment or explanation. It has given rise to a number of philosophical problems; I shall discuss three of these. My principal concern will be with what has been called the logical problem of conditionals, a problem that frequently is ignored or dismissed by writers on conditionals and counterfactuals. This is the task of describing the formal properties of the conditional function: a function, usually represented in English by the words "if ... then", taking ordered pairs of propositions into propositions. I shall explain informally and defend a solution, presented more rigorously elsewhere, to this problem.l The second issue - the one that has dominated recent discussions of con· trary-to-fact conditionals - is the pragmatic problem of counterfactuals. This problem derives from the belief, which I share with most philosophers writing about this topic, that the formal properties of the conditional function, together with all of the facts, may not be sufficient for determining the truth value of a counterfactual; that is, different truth values of conditional state­ ments may be consistent with a single valuation of all nonconditional state­ ments.
    [Show full text]
  • An Analysis of Use of Conditional Sentences by Arab Students of English
    Advances in Language and Literary Studies ISSN: 2203-4714 Vol. 8 No. 2; April 2017 Flourishing Creativity & Literacy Australian International Academic Centre, Australia An Analysis of Use of conditional Sentences by Arab Students of English Sadam Haza' Al Rdaat Coventry University, United Kingdom E-mail: [email protected] Doi:10.7575/aiac.alls.v.8n.2p.1 Received: 04/01/2017 URL: http://dx.doi.org/10.7575/aiac.alls.v.8n.2p.1 Accepted: 17/02/2017 Abstract Conditional sentences are made of two clauses namely “if-clause” and “main clause”. Conditionals have been noted by scholars and grammarians as a difficult area of English for both teachers and learners. The two clauses of conditional sentences and their form, tense and meaning could be considered the main difficulty of conditional sentences. In addition, some of non-native speakers do not have sufficient knowledge of the differences between conditional sentences in the two languages and they tried to solve their problems in their second language by using their native language. The aim of this study was to analyse the use of conditional sentences by Arab students of English in semantic and syntactic situations. For the purpose of this study, 20 Arab students took part in the questionnaire, they were all studying different subjects and degrees (bachelor, master and PhD) at Coventry University. The results showed that the use of type three conditionals and modality can be classified as the most difficult issues that students struggle to understand and use. Keywords: conditional sentences, protasis and apodosis, mood, real and unreal clauses, tense-time 1.
    [Show full text]
  • A Note on Conditionals and Restrictors∗
    A note on conditionals and restrictors∗ Daniel Rothschild Introduction Within linguistic semantics, it is near orthodoxy that the function of the word `if' (in most cases) is to mark restrictions on quantification. Just as in the sentence `Every man smokes', the common noun `man' restricts the quantifier `every', in the sentence `Usually, if it's winter it's cold', `it's winter' acts as a restrictor on the situational quantifier `usually'. This view, originally due to Lewis (1975), has been greatly extended in work by Heim (1982) and, most notably, Kratzer (1981, 1986) into a rich theory of almost all uses of the word `if'. I call this the restrictor view of `if'. Despite its linguistic prominence, this view of the word `if' has played little role in the philosophical discussion of conditionals. Fairly recent philosophical surveys such as Bennett's (2003) book-length introduction or Edgington's (1995; 2008) review articles do not even mention the restrictor view. Stranger still, in his seminal work on conditionals and probability, Lewis (1976, 1986) does not mention the restrictor view which he pioneered, despite the intimate relation noted later by Kratzer (1986).1 This paper tries to fill in the gap left by these omissions.2 I make four main points. First, I argue that given the current state of things our best bet is to accept the `restrictor view' and to assume that `if' is not ambiguous, so ∗This paper was written for a conference in honor of Dorothy Edgington at the Institute of Philosophy, London in May 2011. I am grateful to Dilip Ninan, Scott Sturgeon, and Seth Yalcin for useful discussion of this topic, and particularly to Justin Khoo, whose recent draft (cited below) prompted me to think about these issues.
    [Show full text]
  • Probability of Conditionals in Modal Semantics Contents
    Lecture Notes: Probability of Conditionals in Modal Semantics Justin Khoo and Paolo Santorio November 4, 2018 Contents Contents 1 1 Foundations of modal and conditional semantics and Stalnaker’s Thesis 5 1.1 Beginnings: the material conditional . 6 1.2 Strict and variably strict conditionals . 7 1.3 Restrictor Theory . 11 1.4 Stalnaker’s Thesis . 13 2 Triviality, 1/2: closure-based triviality proofs 17 2.1 A warm up to Lewis . 18 2.2 Lewis’s first triviality result . 19 2.3 Hájek’s generalization . 21 2.4 Bradley-style triviality proofs . 24 2.5 General morals: triviality and informational inferences . 27 2.6 Generalizing beyond conditionals: Russell and Hawthorne . 28 3 Triviality, 2/2: single probability triviality proofs 31 3.1 Fitelson 2015 . 31 3.2 Stalnaker 1976 . 32 3.3 Denying CSO? . 36 3.4 The Wallflower result . 39 1 2 Contents 4 Resisting Triviality 41 4.1 Strategy 1: nihilism . 41 4.2 Strategy 2: context dependence (overview) . 47 4.3 Strategy 3: denying Ratio or closure . 51 5 Tenability 57 5.1 Semantics and indeterminacy . 57 5.2 Tenability, v1 . 59 5.3 Generalizing . 64 6 Empirical Failures of the Thesis 71 6.1 The counterexamples . 71 6.2 Diagnosing . 72 6.3 Local and Global . 73 6.4 Generalizing Stalnaker . 74 7 Triviality for Counterfactuals 77 7.1 Williams’ result . 77 7.2 A collapse result for counterfactuals . 79 Bibliography 83 Overview These notes explore the relationship between natural language conditionals and probability, with particular emphasis on theories of conditionals in contempo- rary modal semantics.
    [Show full text]
  • Insubordinate Conditional Clauses Formed by Japanese Conjunction
    International Journal of Linguistics, Literature and Translation (IJLLT) ISSN: 2617-0299 (Online); ISSN: 2708-0099 (Print) DOI: 10.32996/ijllt Journal Homepage: www.al-kindipublisher.com/index.php/ijllt Insubordinate Conditional Clauses Formed by Japanese Conjunction -ba Sang Zhonglin PhD student, Graduate School of Humanities, Nagoya University, Nagoya, Japan Corresponding Author: Sang Zhonglin, E-mail: [email protected] ARTICLE INFORMATION ABSTRACT Received: December 15, 2020 Insubordination describes the phenomenon that a subordinate clause is used Accepted: February 10, 2021 independently as a main clause. Insubordinate clauses endorse discourse functions Volume: 4 alone without connecting with any apodosis. Many researchers studied this Issue: 2 phenomenon from a typology perspective, clarifying the discourse functions and DOI: 10.32996/ijllt.2021.4.2.6 forming mechanism. However, those studies pursuit the cross-language features too much, investigating large numbers of languages and source constructions. As a result, KEYWORDS their conclusion may not fit a specific language or construction. This paper aims to verify and complement the classification of one of the typology studies: Evans (2007), Insubordination, conditional based on the investigation of the insubordinate conditional clauses formed by clauses, Japanese, -ba, discourse Japanese conjunction -ba, through the Balanced Corpus of Contemporary Written functions Japanese (BCCWJ). The investigation result showed that Evans’ (2007) classification fit the insubordinate -ba-clauses to some extent with a slight adjustment. Specifically, the types of “indirection and interpersonal control” and “modal insubordination” were combined as Type A, which was named “modal insubordination”. Meanwhile, a new discourse function, “requirement of further information” was added to the other type, “signaling presupposed material” to compose Type B, which was named “signaling presupposed material”.
    [Show full text]
  • Conditionals, Inference, and Evidentiality
    Conditionals, Inference, and Evidentiality Karolina Krzyżanowska1, Sylvia Wenmackers1, Igor Douven1, and Sara Verbrugge2 1 Faculty of Philosophy, University of Groningen, Oude Boteringestraat 52, 9712 GL Groningen, The Netherlands 2 Department of Psychology, University of Leuven, Tiensestraat 102, 3000 Leuven, Belgium Abstract. At least many conditionals seem to convey the existence of a link between their antecedent and consequent. We draw on a recently proposed typology of conditionals to revive an old philosophical idea according to which the link is inferential in nature. We show that the proposal has explanatory force by presenting empirical results on two Dutch linguistic markers. 1 Introduction Although various theories of conditional sentences have been proposed, none of them seems to account for all the empirical data concerning how people use and interpret such sentences.3 It is almost universally agreed that no theory of conditionals counts as empirically adequate if it validates sentences like these: (1) a. If badgers are cute, then 2 + 2 = 4. b. If weasels are vegetables, then unicorns hold Frege in particularly high esteem. It is easy to understand why people are reluctant to accept conditionals like (1a) and (1b): the antecedents of those conditionals have nothing to do with their consequents. And it seems that using a conditional construction is meant to convey the existence of some sort of link between the content of the if-clause and the content of the main clause. But what kind of link might this be? According to an old philosophical idea, the link is inferential in nature. If this idea is currently unpopular, at least in philosophy, that may be due to the fact that theorists have failed to recognize that the inferential connection need not be of one and the same type.
    [Show full text]
  • Chapter 8: the Logic of Conditionals
    Chapter 8: The Logic of Conditionals § 8.1 Informal methods of proof Conditional elimination This method of proof is also known by its Latin name, modus ponens (literally, “method of affirming”—roughly, having affirmed the antecedent of a conditional, you may affirm the consequent). From P and P → Q , you may infer Q. Biconditional elimination This is sometimes called “modus ponens for the biconditional.” From P and P ↔ Q , you may infer Q. From P and Q ↔ P , you may infer Q. Some handy equivalences Contraposition P → Q ⇔ ¬Q → ¬P The “conditional – disjunction” equivalence P → Q ⇔ ¬P ∨ Q The “negated conditional” equivalence ¬(P → Q) ⇔ P ∧ ¬Q The “biconditional – conjunction” equivalence P ↔ Q ⇔ (P → Q) ∧ (Q → P) The “biconditional – disjunction” equivalence P ↔ Q ⇔ (P ∧ Q) ∨ (¬P ∧ ¬Q) In some systems of deduction for the propositional portion of FOL, these equivalences are used as rules. In the system F, and in Fitch, these are not going to be rules. In fact, we will be using Fitch to prove these equivalences. Still, it is useful to be aware of them. Note that the equivalence symbol ⇔ is not a connective of FOL, but a symbol we use in the “metalanguage” (in this case, English, the language in which we talk about FOL), and the statements of equivalence are not FOL sentences. For a useful chart of tautological equivalences, see the Supplementary Exercises page on the course web site. Look under the listings for Chapter 7. The method of conditional proof This very important method of proof is a way of establishing conditional sentences. In using this method, we make a provisional assumption, P, and deduce some consequences of it.
    [Show full text]